**Compound Interest Formula**

The interest is added back to the principal sum in order that interest can be earned on that additional interest during the next cyclical period. To understand the **Compound Interest Formula** let’s take a look at this article where the CI Formula along with derivation furnished. The basic the conception as well as Compound Interest Formula for Quarterly/Half Yearly and also its illustrations provided on this page.

The major benefit of Compound Interest Formula is that Compound Interest Formula for Excel is used for debit as well as credit aspects in the terms of financial world. Compound Interest Formula is also used in Excel or Java. To know more about the Compound Interest Formula Derivation and its uses, individuals need to scroll down this page which is well prepared by the Dedicated and inspired team of recruitmentresult.com

**Compound Interest Formula**

__Formula Of Compound Interest__

The formula for annual compound interest, including principal sum, is:

Compound Interest Formula: A = P (1 + r/n) ^{(nt)}

Where:

- A = amount of money accumulated after n years, including interest.
- P = principal amount (the initial amount you borrow or deposit)
- r = annual rate of interest (as a decimal)
- t = number of years the amount is deposited or borrowed for.
- n = number of times the interest is compounded per year

Check Out: __Compound Interest Problems With Solutions__

__Fundamental Compound Interest Formulas__

Compound Interest Formula For Monthly:

Amount = P (1 + R / 100)^{ n}

Compound Interest Formula For Half-yearly:

Amount = P (1 + (R/2)/ 100)^{ 2n}

Compound Interest Formula For Quarterly:

Amount = P (1 + (R/4)/ 100)^{4n}

When Rates are different for different years, say R1%, R2%, R3% for 1st, 2nd and 3rd year respectively:

Amount = P (1 + R _{1} / 100)^{ (}1 + R _{2} / 100)^{ (}1 + R _{3} / 100)

Present worth of Rs. x due n years hence is given by:

Present Worth = X / (1 + R / 100)

Read Now: Discount Formulas – Rules With Examples

__Compound Interest Formula Derivation__

__How to calculate the Compound Interest__?

Write P for your starting principal, and r for the rate of return expressed as a decimal to find out the formula for future value (So if the interest rate is 5%, r equals .05). To know your balance go through the following table;

Year | Balance |

Now | P |

1 | P + rP |

2 | (P + rP) + r(P + rP) |

This starts to get messy in a hurry. But you can simplify it by noticing that you can keep pulling out factors of (1 + r) from each line. If you do that, the balances collapse to a simple pattern:

Year | Balance |

Now | P |

1 | P(1 + r) |

2 | P(1 + r)^{2} |

Check Here: __Permutation And Combination Questions And Answers__

__How to calculate compound interest In Math__?

Calculating the Total Value of the Compound Interest Formula For Deposit

P (1+ i/n)nt

Step 1: 10,000 (1+0.05/4)4×10

Step 2: 10,000(1+0.0125)40

Step 3: 10,000 (1.0125)40

Step 4: 10,000 (1.64361946349)

Step 5: 16436.1946349

We can round of this total to Rs. 16,436.19. So the compound interest earned after 10 years is Rs. 6,436.19.

__Calculating the Interest Earned__

We can also arrive at this figure using the formula for compound interest earned. We can substitute the numbers for letters as seen below:

P [(1+ i/n)^{nt} -1]

Step 1: 10,000 [(1+0.05/4)4×10 -1]

Step 2: 10,000 [(1+0.0125)40-1]

Step 3: 10,000 [(1.0125)40-1]

Step 4: 10,000 [(1.64361946349) -1]

Step 5: 10,000 (0.664361946349

Step 5: 6436.1946349

We can now add this interest earned to the principal amount to find out the value of the deposit. The maturity value will be Rs. 16,436.19.

Check Out Here: __Probability Questions With Answers__

__Compound Interest Formula in Excel __

__How to calculate Compound Interest in Excel__

Generic formula

=FV (rate,nper,pmt,pv)

__Explanation__

To calculate compound interest in Excel, you can use the FV function.

This example assumes that $1000 is invested for 10 years at an annual interest rate of 5%, compounded monthly.

In the example shown, the formula in C10 is:

=FV (C6/C8,C7*C8,0,-C5)

You Can Also Check: __Maths Formulas__

__Compound Interest Formula Derivation__

__Annual Compound Interest Formula __

To calculate the compound interest for a number of years together, we need to multiply P(1+i) to the power of the number of years of the deposit. So we end up with this formula:

P (1+ i/n)^{n}

__Compound Interest Formula Half-Yearly, Quarterly, Monthly __

If you are earning interest multiple times in a year, you need to factor in this number into the equation. So the formula generated is:

P (1+ i/n)^{nt}

This formula can also be used for instances where the interest is compounded once every two years. In this case, n = 0.5, as each year is calculated as half.

__Compound Interest Formula In Java__

__How to calculate compound interest In Java__?

In simple, compound interest is a interest on interest, It’s the result of reinvesting.

The formula to find the compound interest

A=P (1 + r/n)^{nt}

Where,

A =” Ending Amount “

P =” Principal “

R =” Interest Rate “

N =” Number of compounding a year “

T =” Total Number Of Years “

__Java Program to calculate Compound Interest__

We take principal (p), time (t), rate of interest (r) and the number of times the interest is compound (n) as inputs. Amount is calculated using the formuale p * ( 1 + r/n )nt. In Java, the Math.pow() function is used to calculate powers. For example, to calculate 32, we use Math.pow(3,2). After finding amount, we find interest by subtracting principal.

Sample Execution:

__Input__:

p = 3400

t = 3

r = 4

n = 2

__Output__:

Compound Interest is 2475200.0

Amount is 2478600.0

Check Here: __Problems on Ages Question & Answers__

__Compound Interest Formula Derivations__

The basic formula for Compound Interest is: FV = PV (1+r)^{n}

FV = Future Value,

PV = Present Value,

r = Interest Rate (as a decimal value), and

n = Number of Periods

FV = PV (1+r)^{n} | Find the Future Value when we know a Present Value, the Interest Rate and number of Periods. |

PV = FV / (1+r)^{n} | Find the Present Value when we know a Future Value, the Interest Rate and number of Periods. |

r = ( FV / PV )^{1/n} – 1 | Find the Interest Rate when we know the Present Value, Future Value and number of Periods. |

n = ln (FV / PV)ln(1 + r) | Find the number of Periods when we know the Present Value, Future Value and Interest Rate |

__How to Calculate Compound Interest on Recurring Deposit__?

When it comes to Recurring Deposits, interest amount is compounded every quarter. This is then added up and the final amount that customers receive can be determined. The formula used to calculate compound interest is as follows-

A = P (1 + r/n) ^{nt}

For example,

Sita has made an initial investment of Rs.1 lakh for a period of 5 years. The interest rate applicable is 8%. By using the above formula, the final amount that he will get is Rs.1.5 lakh.

START Your Practice With Online: __Mathematics Quiz__

__How to Calculate Recurring Deposit Maturity Amount & Interest__?

__Calculating Recurring Deposit Maturity Amount__:

Now, we will calculate amount (A) from above formula for each installment we pay, starting from first month to 12th month and then add all of them. So the final maturity amount will be

A = A1+A2+A3+…..+A12

A1, A2, A3,,,A12 are the maturity amount for respective installment

__Compound Interest Equations__

__Compound Interest Equation and Calculation__

Period | Deposit Balance |

Investment | P |

Year 1 | P + iP |

Year 2 | (P+ iP) + i(P+iP) |

To collapse this formula, we can pull out factors of (1+i). Simply substitute iP with (1+i) to get the following:

Period | Deposit Balance |

Investment | P |

Year 1 | P(1+i) |

Year 2 | P(1+i)2 |

Year 3 | P(1+i)3 |

Get Best Answer: __How to Prepare for Maths__

__Compound Interest Calculator__

__Simple Interest vs. Compound Interest__

Period | Deposit 1 – Compound Interest | Deposit 2 – Simple Interest | Difference |

Year 1 | Rs. 500 | Rs. 500 | Rs. 0 |

Year 2 | Rs. 1,025.00 | Rs. 1,000 | Rs. 25 |

Year 3 | Rs. 1,576.25 | Rs. 1,500 | Rs. 76.25 |

Year 4 | Rs. 2,115.06 | Rs. 2,000 | Rs. 115.06 |

Year 5 | Rs. 2,762.82 | Rs. 2,500 | Rs. 762.82 |

Year 6 | Rs. 3,400.96 | Rs. 3,000 | Rs. 400.96 |

Year 7 | Rs. 4,071.00 | Rs. 3,500 | Rs. 571.00 |

Year 8 | Rs. 4,774.55 | Rs. 4,000 | Rs. 774.55 |

Year 9 | Rs. 5,513.28 | Rs. 4,500 | Rs. 1,013.28 |

Year 10 | Rs. 6,288.95 | Rs. 5,000 | Rs. 1,288.95 |

__Compound Interest with Monthly Contributions__

Period | Investment Breakdown | Investment + Interest Accumulated | Interest Earned | Total Value of Deposit |

Year 1 | 10,000 + 12,000 | 22,000 | 1,100 | 23,100 |

Year 2 | 10000 + (12000 x 2) + 1,100 | 35,100 | 1,755 | 36,855 |

Year 3 | 10000 + (12000 x 3) + (1,100 +1,755) | 48,855 | 2,442.75 | 51,297.75 |

Year 4 | 10000 + (12000 x 4) + (1,100 +1,755 + 2,442.75 ) | 63.297.75 | 3164.87 | 66,462.64 |

Year 5 | 10000 + (12000 x 5) + (1,100 +1,755 + 2,442.75 + 3164.87 ) | 78,461.75 | 3,923.13 | 82,385.77 |

__Compound Interest Formula With Example__

Here we have provided Compound Interest Formula Shortcut with essential Compound Interest Formula illustrations. Have a look here;

__Example -1__

If an amount of $5,000 is deposited into a savings account at an annual interest rate of 5%, compounded monthly, the value of the investment after 10 years can be calculated as follows…

__Solution __

P = 5000. r = 5/100 = 0.05 (decimal). n = 12. t = 10.

If we plug those figures into the formula, we get:

A = 5000 (1 + 0.05 / 12) ^ (12(10)) = 8235.05.

So, the investment balance after 10 years is $8,235.05.

__Example -2__

An investment earns 3% compounded monthly. Find the value of an initial investment of $5,000 after 6 years.

__Solution__

Determine what values are given and what values you need to find.

Earns 3% compounded monthly: the rate is r=0.03r=0.03 and the number of times compounded each year is m=12m=12

Initial investment of $5,000: the initial amount is the principal, P=5000P=5000

6 years: t=6t=6

You are trying to find AA, the future value (the value after 6 years). Now apply the formula with the known values:

A = P (1 + r/m) ^{(mt)}

= 500(1 + 0.03/12) ^{12 * 6}

= 5984.74

__Example -3__

Find the amount of $ 8000 for 3 years, compounded annually at 5% per annum. Also, find the compound interest.

__Solution__

Here, P = $ 8000, R = 5 % per annum and n = 3 years.

Using the formula A = $ P(1 + R/ 100)ⁿ

amount after 3 years = $ {8000 × (1 + 5/100)³}

= $ (8000 × 21/20 × 21/20 × 21/20)

= $ 9261.

Thus, amount after 3 years = $ 9261.

And, compound interest = $ (9261 – 8000)

Therefore, compound interest = $ 1261.

__Example -4 __

Find the compound interest on $ 6400 for 2 years, compounded annually at 7¹/₂ % per annum.

__Solution__

Here, P = $ 6400, R % p. a. and n = 2 years.

Using the formula A = P (1 + R/100)ⁿ

Amount after 2 years = [6400 × {1 + 15/(2 × 100)}²]

= $ (6400 × 43/40 × 43/40)

=$ 7396.

Thus, amount = $ 7396

and compound interest = $ (7396 – 6400)

Therefore, compound interest = $ 996.

__Example -5__

Find the amount of $ 12000 after 2 years, compounded annually; the rate of interest being 5 % p.a. during the first year and 6 % p.a. during the second year. Also, find the compound interest.

__Solution__

Here, P = $12000, p = 5 % p.a. and q = 6 % p.a.

Using the formula A = {P × (1 + P/100) × (1 + q/100)}

amount after 2 years = $ {12000 × (1 + 5/100) × (1 + 6/100)}

= $ (12000 × 21/20 × 53/50)

=$ 13356

Thus, amount after 2 years = $ 13356

And, compound interest = $ (13356 – 12000)

Therefore, compound interest = $ 1356.

__Benefits of Compound Interest Formula__

Compound interest is used for both debit and credit aspects of the financial world. Listed below are some of the investments and credit options that use compound interest. In the field of Investments Compound Interest Formula is used for Savings Accounts, Fixed Deposits, Recurring Deposits, Other Certificates of Deposits, Reinvested Dividend Stocks, and Retirement Funds and also for Debt as Loans, Credit Cards, and Mortgages.

__Note __

We have provided almost Compound Interest Formula on this article. Candidates who want to know more about math fundamental formulas are suggested to regular visit on our website as we will deliver you updated information. If you have any query you can leave your precious comment in the below provided comment box. Our expert team members solve your queries as soon as possible.

__Something That You Should Put An Eye On:__

Aptitude Questions & Answers | Quantitative Aptitude Quiz |

Current Affairs for competitive exams | Online Quiz |

How to Prepare for Reasoning | How To Prepare For GK |